Particle accelerators generally are grouped into different categories according to their fundamental concepts:    1) Those that use constant electrostatic fields such as Van de Graaff accelerators;    2) Those that make use of radiofrequency cavities in a straight line such as linear accelerators;    3) Those that use the electric fields induced by a time varying magnetic field to accelerate a particle such as the betatron; and    4) Circular accelerators that recirculate the beam of particles through a radiofrequency cavity to reach a desired energy such as a cyclotron, synchrotron, microtron, racetrack microtron or Rhodotron™.
Different names have been used to describe different combinations of the ideas represented by these categories and the concepts they represent, as they have been perceived to be advantageous in different applications. Many are discussed in books about accelerator design such as M. S. Livingston and J. P. Blewett, “Particle Accelerators”, McGraw Hill Book Company, Inc., New York, 1962. They all apply the fundamental Maxwell equations and particle dynamics in magnetic and electric fields to accelerate particles and to form accelerated beams.
Most particle accelerators having a degree of complexity require methods and systems for monitoring and controlling the beams they produce. Such systems are often referred to as diagnostic systems or simply “diagnostics”. In the case of the novel accelerator partly described herein and more fully described in the co-pending application, “Methods and Systems for Accelerating Particles Using Induction to Generate an Electric Field with a Localized Curl” by William Bertozzi, Stephen E. Korbly and Robert J. Ledoux, the specific characteristics of the accelerator introduces unique requirements for the processes of monitoring and controlling the beam. Because the beam mostly travels inside an electrically conductive enclosure except at an accelerating gap, it is not readily accessible for diagnostic measurements. Conventional methods of monitoring a beam in such a case include the use of intercepting beam stops located at different positions in the beam orbits or probes that can sense the beam location and/or size and that can be moved within the vacuum chamber. These conventional techniques require vacuum couplings and/or feedthroughs for movable probes. Disclosed herein are techniques and apparatus that are particularly adapted to the novel accelerator design. Certain of these techniques and apparatus also are suitable for use with other accelerator types.